Negative impedance



Aug. 14, M' M' DOLMAGE.

NEGATIVE IMPEDANCE Filed oct. 27. 1932l I N VEN TOR.

Patented ug. 14, 1934 PATENT OFFICE NEGATIVE IBIPEDANCE Mihran M. Dolmage, Washington, D. C.

Application October 27,

6 Claims.

This invention relates to a new combination in the electrical art, a negative impedance.

The term impedance, in the present invention, is taken in its broadest general sense. It may include resistance, capacity, and inductance elements. These may be associated in any complex electrical network we may choose. We may also have a multiplicity of resistance, capacity and inductance elements, in periodically recurring structures. The inductance, capacity and resistance elements may be in series or in shunt combination. The various impedance elements may also be those in a natural transmission line, with uniformly distributed constants. The term negative impedance, as herein used, is also taken in its broadest general meaningin that if the complex impedance as just dened is included in an electrical circuit, the present invention shows a method whereby its exact negative image may be designed, so that if this negative impedance and the originally given impedance are included in a circuit in series relation, for instance, the combined impedance will be zero ohms, and what is more important, this neutralization will `holdsimultaneously for all frequencies, from a few cycles to a million cycles or more. There is no novelty or diiculty involved in the present art, given any electrical circuit, to iinding a second circuit which when Wired in series with the rst circuit will completely neutralize the impedance of the first. But such complete neutralization can only be effected for some one given frequency. Where it is necessary to transmit simultaneously a number of frequencies over a given line, or through a given electrical circuit (which is the general case in signaling circuits, both of the wire and wireless types), then none of the ordinary methods ofV neutralization can be applied, as the neutralization with such ordinary methods can be completely eiiected, as above stated, for one frequency only. The neutralization for all other frequencies, is partial, as well known, and when this is the case, the resulting effect as regards all these other frequencies, is designated under the general term of distortion. The elimination of such distortion is extremely important, particularly in the long cables used in the communication art.

In a number of prior applications, I have disclosed for the rst time, certain simple types of "negative impedances. In U. S. A. 1,606,350, Nov.

9, 1926, granted to me, is shown a negative resistance; in U. S. A. 1,815,838, July 21, 1931, also granted to me, is shown a negative capacity; in

1932, Serial N0. 639,919

U. S. A. 1,903,610, April 11th, 1933, is shown a negative inductance. All of these devices are the negatives of single electrical elements. In U. S. A. 1,910,151, May 23, 1933, I have shown it negative anti-resonant circuit, which contains 6 a circuit, we may arrange for partial neutralization, if we so wish. If, for instance, we wish fifty per cent neutralization of the impedance elements included in a circuit, we can accomplish this result also, such neutralization being equally y effective at all frequencies.

The rnovel features of znyinvention are pointed out in the appended claims. he invention itself will be best understood by reference to the drawing and discussion given hereunder.

Fig. l of the drawing shows the general idea underlying the use of my method. Fig. 2 shows the impedance (Z2) with all its components, whose negative image or counterpart (-Zz) is reproduced by the arrangement shown on Fig. 1 of the drawing. Fig. 3 shows in graphic form the characteristics of the negative impedance device designed to simulate the negative of a telephone line.` As a matter cf interest, the characteristics oi said telephone line, with reference to frequency, are also shown in this same iigure in dotted line. It will be seen how, for each frequency, the combined impedance of the various elements included as part of the negative impedance, is the exact negative image or counterpart of the impedance of a telephone line. Fig. 4 shows a particular method of carrying out my invention, using as a negative resistance the particular type of circuit and apparatus covered in U. S. A. Patent No. 1,606,350, granted to me.

The apparatus, where it is shown on Fig. 1 of the drawing, represents, when viewed from terminals (1, 2), a negative impedance within the meaning already specified. Element (3) is an ordinary resistance. Element (4) is a negative resistance. It may be of any type known to the art. It may be, for instance, of the type first disclosed by Dr. Hull (U. S. A. Patent 1,313,187), or preferably, it may be of the type -irst disclosed by me (U. S. A. Patent 1,606,350) and reproduced in Fig. 2 of the drawing, wired across the terminais (7, 8). The character of the elements (6), (ri), (8), (9) and (l0), which form part of a complex impedance have been shown in accordance with the usual conventions. The impedances involved in this case are thus five in number. It is proposed to construct an electrical sys-tern which will have the impedance (+22) the exact negative for the impedance (+22) for any frequency between a few cycles to a million cycles, or more. The impedance (+22) Awe 'are referring to here, is the impedance of the entire combination of the five diierent elements '-R1, R2, R3, L3 and C2 as seen or measured from terminals (13, 14) of Fig. 2 of the drawing. The invention shows a method whereby an impedance 22) may be constructed.

Since the expression for the impedance (+21) connected to terminals (13, le). of Fig. 1 ofthe drawing, as a function of frequency is quite complex, we will not develop it, in order to 'avoid unnecessary complications in lexposition of the subject. We will simply assume that (+21), the general expression for this impedance, varies in some complex fashion to frequency, that for some one frequency it has a resistance component and a reactance component, such reactance compo,- nent being inductive or capacitive, as the case may be, depending upon the particular value of the frequency considered. If we write the expression for the impedance for the circuit shown on Fig. 1 of the drawing, as measured from terminals (1, 2), we nd it is equal to R+(R+Z1) Z1 where 21 is the impedance of the combination shown connected to terminals (13, 14) of Fig. 1 of the drawing. We so choose the constitutive elements of the impedance (+21) of Fig. 1 of the drawing with respect to the constitutive elements of the impedance (+22) of Fig. 2 of the drawing, that the following relationis satisfied for the two corresponding or inverse impedances (+21) and (+22).

(Z) Z1 y In order to illustrate the method used in constructing the combination of impedances (+21) knowing the constitutive elements of the impedance (+22), the corresponding elements in the two impedance combinations have been given the same numerical designations on Fig. l and Fig. 2 of the drawing. Element 6 of the impedance combination of Fig. 2 of the drawing is in shunt across terminals (13, 14); the corresponding element 6 of Fig. 1 of the drawing is wired in series, across terminals (13, 14), of Fig. 1 of the drawing, as shown. The parallel elements (7) (8), of Fig. 2 of the drawing, correspend with two series elements (7) (8) of Fig. 1 of the drawing, the resistance elementbeing matched by another resistance element, but the capacity element being "matched by an inductance element. The parallel elements (9) (10) of Fig. 2 of the drawing, (a resistance in parallel to the inductance), are matched on Figl of the drawing, by elements (9) and (10) consisting of the series combination of a resistance and a condenser. in the impedance (+22), a corresponding constitutive element was chosen to form part of the impedance combination, (Z1) of Fig. l of ther drawing, in the noa-nner described and as illustrated on the drawing. In general, the networks Thus, for each element comprising these two impedances (+21) and (+22), will be designated as inverse networks. If the constitutive elements of the two networks 0f Fig. 1 and Fig. 2 of the drawing had been chosen as just described, then the general equation (2), relating together the impedances (+21) and (+22) would hold, provided further, certain numerical relationships are established as indicated in detail hereunder. Another way of eX- pressing'V this general equatiomwh'ich as will be seen hereunder, holds true equally for all frequencies, would be- In order to indicate the practicability of building two inverse networks of the general type indicated, we proceed to choose the impedances Z4, 25,and-Z, of Fig.f.l= of the drawing, to correspond to .the originally given admittances of Fig. 2 ofthe drawing, as follows:

24=impedance of ftheA corresponding element 6 of Fig. 1 of the drawing. Yszadrnittance of elements 2 of the drawing; l Y

25=impedance of lthe corresponding elements ("1) and (8) of Fig. 1 of the drawing.

:(7) and (s) of Fig.

Ye=admittanceof elements (9,) and (10) of 2 of the drawing.

, ZG--impedance ofthe corresponding elements of (9) and (1 0) of Fig. 1 of the drawing.

, The expression-for the total admittance (Y2) of 'the combination of imp'edances'connected to v terminals (711.3, 14) of Fig. 2 of the drawing is YY Yrs-FY Theexpression for'th'e total impedance (+21) of the corresponding elements of Fig. 1l of the drawing is given byy. Z`5Z6 Replacing in the equation (8), the values of (Z4), (Z5) and (2s) in 4function of the primary admittances(Y-.), (Ys) and`v Ys) vas given by the above equations (4) (5) and`(6), respectively, we

The above relation is absolutely independent of frequency, provided, of course, we can effectively satisfy equations (4) (5) and (6) without discrimination as to frequency. Considering rst the twofcorresponding elementsv (6),.each of which is Ia resistance', there can of course be no difficulty as to frequency.discrimination-.here and.

equation (4) can be satisfied exactly. Considering, next, the admittance of elements ('7) and (8) of Fig. of the drawing, evidently- Suppose we choose the corresponding elements ('7) and (8) in Fig. 1 of the drawing, as follows- R2 Resistance R2 Inductance= C2122 The impedance Z5 is thus equal to 12H-R2 are) R2 JP 2- R2 JP 2 Hence the ratiois absolutely independent of frequency.

Considering, next, the admittance of elements (9) and (10), Fig. 2 of the drawing- 1 1 R3 JpLa Suppose We choose the corresponding elements in Fig. 1 of the drawing, as follows- 1 2 Res1stance-R R3 Capacity =3 The impedance Ze is given by- R2 1 (14) Za E3 J P Ca The ratio as obtained by dividing equation (14) by equation (13), is equal, then, to-

and is absolutely independent of frequency.

We thus have been able to construct an impedance (-|-Z1), which is equal to as shown in equation (2), for all values of frequency. It follows, therefore, that for all values of frequency, the impedance of a combination of elements wired to terminals (1), (2) of Fig. 1 of the drawing, is equal to- We then connect this inverse network Z1 into a circuit such as is shown in Fig. 1 of the drawing, in conjunction with a system of two positive and one negative resistances, all these resistances having substantially the same numerical value.

The method above described is absolutely general, and is applicable regardless of the number or complications of the elements involved in the impedance combination (Z2), whose negative image or counterpart must be obtained. It is applicable to an impedance or network system containing any number of elements, instead of just five elements, as assumed on Fig. 3 of the drawing. It can also be applied to extended circuits with distributed constants, such as a high tension line or a transmission line, used in the signalling art. In all cases the inverse network (-'{-Z1) must be constructed with as many elements as there are included in the impedance (+22) as originally given. Since most reactances, in practice, also have resistance components unavoidably, the negative impedances which can be built, using the method first disclosed in these specifications, can be made to match perfectly any type of electrical circuit; even those with distributed constants can be so matched, provided the number of discreet iinpedanee elements representing such circuit with distributed constants is adequately chosen, in accordance with indications of the present art.

It will be noted that the numerical value of (R), in all the equations, is indeterminate. It is, therefore, possible to so choose (R) that the most convenient or practical value will result for the various impedance elements that must be provided.

An extremely interesting application is shown on Fig. 3 of the drawing. On that figure is shown, in full line, the reactance-frequency character-- istics of the negative counterpart of a natural telephone line, and, in dotted line, the actual reactance-frequency characteristics of the natural line itself.

It was not possible, up to the present time, to construct the negative image of a reactance having also a resistancecomponent. The negative capacity device first disclosed by me in U. S. A. 1,815,838 and the negative inductance device, first disclosed by `me in U. S. A. 1,903,610, April 11, 1933, could only be usedto match a positive capacity. and a positive inductance, respectively,

kin an approximate manner only, in view of the fact that all capacities and inductances that are commercially available, possess resistance components. With the method, as first disclosed in these specifications, it is possible to obtain a more perfect neutralization of the inductances and the capacities that are met with in practice. Furthermore, the present invention is the rst showing how negative images of complex impedances, with a multiplicity of parts, may be obtained.

The invention, as first disclosed in the present specifications, thus opens unlimited possibilities in the way of the application of methods of eliminating distortion in long telephone cables, in radio antennae, radio broadcasting equipment and radio broadcasting receivers. 1n all of the cases just mentioned, the primary problem is the diiculty of avoiding unequal impedance response of the respective circuits involved to currents of different frequency. Even where band filters are used, the response to frequencies involved within the band itself, is almost invariably unequal, resulting in distortion, or lack of fidelity. All such diiiiculties can be immediately overcome with the use of the method outlined hereunder. There seems to be an unlimited field of usefulness for the negative impedance device as hereinabove outlined.

Although the analytical treatment has been Cil carried out to show how the exact negative counterpart (-22), of a complex network having an impedance (+22) can be obtained, vit is apparent that the procedure hereinabove disclosed may be utilized also for obtaining any desired degree of neutralization. For instance, if a negative impedance 22) is wired in series with ka given complex impedance (+22) the totalcircuit impedance will be zero, and it will be zero for all frequencies. However, nothing prevents us from obtaining, say, %r neutralization of the irn- .pedance (+22), said neutralization being equally effective at all frequencies, since we can also .construct a negative impedance (-1/222) which, when inserted in series with the given network, will result in an impedance (+1/222), one-half of the original impedance` It is also evident that negative impedance networks, constructed in accordance with the method iirst disclosed in these specifications, when inserted at equal or unequal intervals in a natural transmission line, will compensate completely for both attenuation and phase distortion. In Fig. 3 of the drawing, the extremely valuable negative reactance-frequency properties of a network built in accordance with the present invention have been shown. These properties are the exact 'cpposite of those of a natural transmission line as'denitely indicated on Fig. 3 of the drawing in dotted line. It should be understood, of course, that similar negative properties for the resistance component are simultaneously developed, though not illustrated on the drawing for purposes of simplification. It is the development of these l negative resistance properties, that is effective in compensating for attenuation distortion, while development of the negative reactance properties, compensates for phase distortion. f

l. An automatic device of impedance (-Z2) having resistance and reactance characteristics exactly opposite and equal in absolute value to that oi a given complex impedance network (+22) comprising a multiplicity of resistance, capacity and inductance elements, said negative equality relation holding true independently of frequency, said automatic device consistingof the combination of a T network of three resistances substantially equal in absolute value, one of which is a negative resistance, with an inverse network"(21) of constant resistance product (R2) so that (2122):(R2) for allvalues of frequency.

2. A two-terminal electrical network of negative impedance (-22), consisting in the combimesses nation of a negative resistance '('-R.)`, in'parallel with the #combination of 'a positive resistance (+R) in series with the impedance (+21) fof a complex network comprising resistance, capacity and inductance elements, theV entire combination being wired in series with a positive resistance (+R), saidcornplex impedance (+21) representing .an inverse vnetworkv of constant resistance product R2 to the impedance (+22) of the given network, substantially as described.

3. A two-terminal electrical network of negative impedance (-22) 'consisting in the combination of a negative resistance (+R.) in parallel with the combination of a positive resistance (+R) in ser-ies with the impedance (+21) of an inverse network comprising resistance, capacity and inductance elements, the entire combination being wired in series with a positive resistance (+R), each element v in network (+21) being matched by a corresponding element in network (+22), so that 21Z2=R2, a series capacity element being matched by a parallel inductance element, a series inductance element by parallel capacity element, a series resistance element by a parallel resistance element, substantially as described.

4. .In series combination with a complex electrical network (22) comprising resistance, capac-` ity and inductance elements, automatic means for completely neutralizing both the resistance and the reactanc'e effects of said electrical network to the ow of electrical currents through said network, said means consisting of the structure described in clairn, equally effective at all frequencies.

5. In an electrical circuit, the parallel combination of a complex yelectrical network (+22) and of a neutralizing impedance network (-Z2), the network (+22) 4comprising resistance, inductance and capacity elements,the neutralizing impedance consisting of automatic means for completely eliminating the eiect of the presence of the network (+22) in said electrical circuit, for all Values of frequency, said means consisting of the structure described in claim 3.

6. A negative impedance network (-Z2), consisting-.of the combination of a T network of three resistances equalin absolute value, one ci which is a negative resistance, with an inverse network, (+21) of constant resistance product R2 so that 125 Z122=R2, for all values of frequency, said inverse network comprising resistance, inductance and capacity elements.

MIHRAN M. DOLMAGE. 

